Picard iterative processes for initial value problems of singular fractional differential equations

DOI10.1186/1687-1847-2014-102zbMath1343.34151OpenAlexW2104684666WikidataQ59323865 ScholiaQ59323865MaRDI QIDQ738453

Yuji Liu, Xiao-Hui Yang

Publication date: 2 September 2016

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2014-102

zbMATH Keywords

initial value problemsingular fractional differential equationPicard iterative methodthe Caputo fractional derivativethe Riemann-Liouville fractional derivative

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) General theory of functional-differential equations (34K05) Differential inequalities involving functions of a single real variable (34A40)

Related Items (10)

A spectral approach to analyze the nonlinear oscillatory fractional-order differential equations ⋮ Picard's iterative method for Caputo fractional differential equations with numerical results ⋮ Certain analysis of solution for the nonlinear two-point boundary value problem with Caputo fractional derivative ⋮ Explicit analytical solutions of incommensurate fractional differential equation systems ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Existence and continuous dependence for weighted fractional differential equations with infinite delay ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Qualitative analysis of dynamic equations on time scales

Cites Work

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• Global existence theory and chaos control of fractional differential equations
• Basic theory of fractional differential equations
• General uniqueness and monotone iterative technique for fractional differential equations
• Theory of fractional functional differential equations
• Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Differential equations of fractional order:methods results and problem —I

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